\(\Gamma _2\)  is physically well-defined, however, it is no longer
geometric. It is not merely a function of the cyclic path, it also
depends on “how fast” the path is traversed in the variable \(t\) .
\(\Gamma _2\)  gives finite numbers for adiabatic paths which do not
encounter crossing points. The situation is similar for all higher
order cumulants. An \(n\) th order \(C_n\)  will lead to a factor of
\(\delta t^n\) , from which \(n-1\)  have to be eliminated to lead to a
\(\Gamma _n\)  which is physically well-defined, albeit, not geometric.
Cumulants constructed this way are known as gauge invariant cumulants,
introduced in the context of the MTP by Souza, Wilkens, and
Martin [1]}.
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